Hybrid analytical–numerical approach for modeling transient wave propagation in Lorentz media

The advent of ultrawideband, short-pulse sources has recently generated renewed interest in the problem of pulse propagation in dispersive media. When one is trying to numerically simulate transient plane-wave propagation through a dispersive medium, the main difficulties are encountered in trying to transform from the frequency domain to the time domain. We develop an asymptotic-extraction technique wherein asymptotic methods are used in conjunction with a fast Fourier transform (FFT) to overcome the limitations of each method. The basic idea behind the asymptotic-extraction technique is to extract and analytically invert as much of the signal as possible. The remainder of the signal is then transformed by use of a numerical FFT. We demonstrate that it is possible to construct functions that possess analytical inverse transforms and also asymptotically model the low- and high-frequency behavior of a field propagating in a single-resonance Lorentz medium. Extraction of the low- and high-frequency responses from the spectral representation for the waveform in essence preconditions the waveform for application of a FFT, thereby significantly reducing the number of sample points required by the FFT. It is also demonstrated that these two extracted functions, whose inverse Fourier transforms are evaluated analytically in terms of known special functions, provide a good approximation for the transient signal for the case of a square-wave-pulse-modulated source, provided that the carrier frequency resides far enough from the absorption band.